Finite Group Databasebeta

← #11808642

Subgroups — #11808642

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×#64086C211yesmaximal, characteristic
3C32×#399C211yesmaximal, characteristic
4#10592684C211yesmaximal, characteristic, complemented
5#10592682C212yesmaximal, complemented
6C4⋊C4×C3⋊Dic3C212yesmaximal, complemented
7#10592647C212yesmaximal
8#10592646C211yesmaximal, characteristic
9C22⋊C4×C3⋊Dic3C212yesmaximal
10#10592355C211yesmaximal, characteristic, complemented
11#10592348C211yesmaximal, characteristic, complemented
12#78018—34nomaximal
13C23×C3⋊Dic3C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2212yes—
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2212yes—
19C2×#3757C2211yescharacteristic
20C2×#3757C2212yes—
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×#3750C2212yes—
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64096—24no—
31#64086—24no—
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38C2×#887—34no—
39C2×#877—34no—
40C3×#399D314yes—
41#4985—34no—
42#4983—38no—
43Dic3×C4⋊C4—38no—
44#4948—38no—
45#4947—34no—
46Dic3×C22⋊C4—38no—
47#4656—34no—
48#4649—34no—
49C24×C32C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2312yes—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3Q814yescomplemented
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2311yescharacteristic
63C2×#634—22no—
64C2×#634—24no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4—24no—
67C32×C22⋊C4—22no—
68C32×C22⋊C4—24no—
69#3757—22no—
70#3757—24no—
71C4⋊(C3⋊Dic3)—24no—
72#3750—22no—
73#3750—24no—
74#3750—22no—
75#3750—24no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3—24no—
78C4×C3⋊Dic3—24no—
79C4×C3⋊Dic3D414yes—
80#2396—91noSylow
81C23×Dic3—34no—
82C22×Dic6—34no—
83C2×C3×C4⋊C4C2×D318yes—
84C2×C3×C4⋊C4C2×D314yes—
85C2×C3×C22⋊C4C2×D318yes—
86C2×C3×C22⋊C4C2×D314yes—
87C2×#217—38no—
88C2×#217—34no—
89C2×C4⋊Dic3—38no—
90C2×Dic3⋊C4—38no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4—38no—
93C2×Dic3⋊C4—34no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—38no—
96C2×C4×Dic3—38no—
97C2×C4×Dic3—34no—
98#887—616no—
99#877—616no—
100C3×#95C2×D314yes—
101C3⋊#95—34no—
102C3⋊#95—38no—
103C3⋊#95—38no—
104C3⋊#95—38no—
105C3⋊#95—38no—
106C23×C32—21no—
107C23×C32—22no—
108C23×C32—22no—
109C23×C32—21no—
110C23×C32C2×Q812yes—
111C23×C32C2411yescharacteristic
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—21no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4C2×D412yes—
121C2×C32×C4#4114yes—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—28no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3⋊Dic3C2×Q812yes—
136C2×C3⋊Dic3C2×Q812yes—
137C2×C3⋊Dic3#4114yes—
138C2×C3⋊Dic3#4112yes—
139#634—28no—
140C2×C4×Q8—91no—
141C2×#117—91no—
142#400—91no—
143#399C3⋊D311yescharacteristic
144#398—92no—
145#396—92no—
146#395—91no—
147#393—91no—
148C4×C4⋊C4—92no—
149C4×C4⋊C4—91no—
150C4×C22⋊C4—92no—
151C24×C3C22×D314yes—
152C22×C3×C4C22×D314yes—
153C22×C3×C4C22×D318yes—
154C22×C3×C4C22×D314yes—
155C22×C3×C4C22×D318yes—
156C22×Dic3—34no—
157C22×Dic3—316no—
158C22×Dic3—34no—
159C22×Dic3—38no—
160C22×Dic3—34no—
161C22×Dic3—38no—
162C22×Dic3—34no—
163C22×Dic3—68no—
164C22×Dic3—68no—
165C2×Dic6—616no—
166C2×Dic6—68no—
167C3×C4⋊C4—28no—
168C3×C4⋊C4—216no—
169C3×C22⋊C4—28no—
170C3×C22⋊C4—216no—
171#217—68no—
172#217—616no—
173C4⋊Dic3—616no—
174Dic3⋊C4—68no—
175Dic3⋊C4—616no—
176Dic3⋊C4—68no—
177Dic3⋊C4—616no—
178C4×Dic3—316no—
179C4×Dic3—68no—
180C4×Dic3—616no—
181C4×Dic3—616no—
182C22×C32—22no—
183C22×C32—24no—
184C22×C32—41no—
185C22×C32—42no—
186C22×C32—41no—
187C22×C32C22×D411yescharacteristic
188C22×C32C22×Q811yescharacteristic
189C22×C32C2×#4112yes—
190C22×C32C2×#4111yescharacteristic
191C22×C32C2×#4112yes—
192C32×C4—22no—
193C32×C4—24no—
194C32×C4—41no—
195C32×C4—42no—
196C3⋊Dic3—22no—
197C3⋊Dic3—24no—
198C3⋊Dic3—22no—
199C3⋊Dic3—41no—
200C3⋊Dic3—42no—
201C3⋊Dic3C22⋊Q814yes—
202C22×Q8—91no—
203C23×C4—91no—
204C4×Q8—184no—
205#117—184no—
206C2×C4⋊C4—91no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—92no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4C2×C3⋊D311yescharacteristic
212C2×C4⋊C4C2×C3⋊D312yes—
213C2×C22⋊C4—91no—
214C2×C22⋊C4—92no—
215C2×C22⋊C4C2×C3⋊D311yescharacteristic
216C2×C22⋊C4C2×C3⋊D312yes—
217C2×C42—91no—
218C2×C42—91no—
219C2×C42—92no—
220C2×C42—92no—
221#95—92no—
222#95—92no—
223#95—92no—
224#95—91no—
225#95—92no—
226#95C2×C3⋊D311yescharacteristic
227C23×C3—24no—
228C23×C3—28no—
229C23×C3—28no—
230C23×C3—24no—
231C23×C3D3×Q818yes—
232C23×C3C23×D314yes—
233C2×C3×C4—28no—
234C2×C3×C4—28no—
235C2×C3×C4—28no—
236C2×C3×C4—24no—
237C2×C3×C4—28no—
238C2×C3×C4—28no—
239C2×C3×C4—28no—
240C2×C3×C4—28no—
241C2×C3×C4D3×D418yes—
242C2×C3×C4#237116yes—
243C2×Dic3—38no—
244C2×Dic3—38no—
245C2×Dic3—38no—
246C2×Dic3—38no—
247C2×Dic3—38no—
248C2×Dic3—316no—
249C2×Dic3—632no—
250C2×Dic3—68no—
251C2×Dic3—64no—
252C2×Dic3—68no—
253C2×Dic3—68no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—68no—
257C2×Dic3—68no—
258C2×Dic3—68no—
259C2×Dic3—68no—
260Dic6—632no—
261C2×C32—42no—
262C2×C32C2×C22⋊Q811yescharacteristic
263C2×C32#52511yescharacteristic
264C2×C32#52912yes—
265C2×C32#53211yescharacteristic
266C2×C32#53312yes—
267C24C22×C3⋊D311yescharacteristic
268C2×Q8—184no—
269C2×Q8—182no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—92no—
273C22×C4—91no—
274C22×C4—94no—
275C22×C4—92no—
276C22×C4—91no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4C22×C3⋊D311yescharacteristic
280C22×C4C22×C3⋊D312yes—
281C22×C4C22×C3⋊D311yescharacteristic
282C22×C4C22×C3⋊D312yes—
283C4⋊C4—22no—
284C4⋊C4—24no—
285C4⋊C4—182no—
286C4⋊C4—184no—
287C4⋊C4—184no—
288C4⋊C4—182no—
289C4⋊C4—184no—
290C22⋊C4—22no—
291C22⋊C4—24no—
292C22⋊C4—182no—
293C22⋊C4—184no—
294C42—94no—
295C42—182no—
296C42—184no—
297C42—184no—
298C22×C3—216no—
299C22×C3—28no—
300C22×C3—48no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3C2×D3×D414yes—
304C22×C3C2×#23718yes—
305C22×C3C2×D3×Q814yes—
306C22×C3D3×#4114yes—
307C22×C3D3×#4118yes—
308C3×C4—216no—
309C3×C4—28no—
310C3×C4—44no—
311C3×C4—48no—
312Dic3—316no—
313Dic3—616no—
314Dic3—68no—
315Dic3—68no—
316Dic3—128no—
317Dic3—124no—
318C32#239611yescharacteristic, complemented, Sylow
319C23—21no—
320C23—22no—
321C23—22no—
322C23—21no—
323C23Q8×C3⋊D312yes—
324C23C23×C3⋊D311yescharacteristic
325Q8—188no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—94no—
340C2×C4—188no—
341C2×C4—182no—
342C2×C4—181no—
343C2×C4—182no—
344C2×C4—181no—
345C2×C4—182no—
346C2×C4—181no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4D4×C3⋊D312yes—
352C2×C4#383014yes—
353C2×C3—48no—
354C2×C3#562218yes—
355C2×C3D3×C22⋊Q814yes—
356C2×C3#564918yes—
357C2×C3#565614yes—
358C2×C3#571614yes—
359C22—22no—
360C22—24no—
361C22—42no—
362C22—41no—
363C22—41no—
364C22C2×D4×C3⋊D311yescharacteristic
365C22C2×#383012yes—
366C22C2×Q8×C3⋊D311yescharacteristic
367C22#41×C3⋊D311yescharacteristic
368C22#41×C3⋊D312yes—
369C4—24no—
370C4—22no—
371C4—41no—
372C4—42no—
373C4—94no—
374C4—182no—
375C4—184no—
376C4—182no—
377C4—362no—
378C4—361no—
379C3#7801814yescomplemented
380C2—42no—
381C2#1059609312yes—
382C2C3⋊D3×C22⋊Q811yescharacteristic
383C2#1059612012yes—
384C2#1059612711yescharacteristic
385C2#1059618711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#399C2
prime radicalC24×C32C23
hypercenter#399C3⋊D3
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #399

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64096C2semidirect
4. #10592684C2semidirect
5. #10592682C2semidirect
6. C4⋊C4×C3⋊Dic3C2semidirect
10. #10592355C2semidirect
11. #10592348C2semidirect
56. C22×C3⋊Dic3Q8semidirect
318. C32#2396semidirect
379. C3#78018semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#640962
C2×#640862
C32×#3992
#105926842
#105926822
C4⋊C4×C3⋊Dic32
#105926472
#105926462
C22⋊C4×C3⋊Dic32
#105923552
#105923482
#780183